Several techniques for sampling a signal below the signal's Nyquist rate are known in the art. Such techniques are commonly known as sub-Nyquist sampling techniques. Example sub-Nyquist sampling schemes are described by Vettereli et al., in “Sampling Signals with Finite Rate of Innovation,” IEEE Transactions on Signal Processing, volume 50, no. 6, 2002, by Tur et al., in “Low Rate Sampling of Pulse Streams with Application to Ultrasound Imaging,” arXiv e-Print archive, March, 2010, and by Gedalyahu et al., in “Multichannel Sampling of Pulse Streams at the Rate of Innovation,” arXiv e-Print archive, April, 2010, which are incorporated herein by reference.
Sampling techniques for time-limited signals are described, for example, by Butzer and Splettstosser, in “A Sampling Theorem for Duration-Limited Functions with Error Estimates,” Information and Control, volume 34, 1977, and by Butzer and Stens, in “Sampling Theory for Not Necessarily Band-Limited Functions: A Historical Overview,” SIAM Review, volume 34, no. 1, 1992, which are incorporated herein by reference.
Some sampling schemes achieve sub-Nyquist sampling rates by exploiting sparsity properties of the sampled signal. Sampling techniques for sparse signals are described, for example, by Mishali and Eldar, in “From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals,” IEEE Journal of Selected Topics in Signal Processing, volume 4, no. 1, 2010, and by Mishali et al., in “Xampling: Analog to Digital at Sub-Nyquist Rates,” CIT Report, volume 5751, 2010, which are incorporated herein by reference, and in PCT International Publications WO 2009/034568 and WO 2010/095083, whose disclosures are incorporated herein by reference.
Sampling schemes for short discrete pulses are described by Candes et al., in “Compressed Sensing with Coherent and Redundant Dictionaries,” arXiv e-Print archive, May, 2010, which is incorporated herein by reference.
The description above is presented as a general overview of related art in this field and should not be construed as an admission that any of the information it contains constitutes prior art against the present patent application.